Page Content April 6^{th} to May 7^{th}, 2021
This programme was interrupted due to the COVID19 pandemic. For more information on the activities held before the intrerruption,
General information
Description
Dynamical systems is a wide area of research which goes beyond mathematics itself, and includes many applications. In addition, the tools are varied and come from most of the classic research lines in mathematics, such as real and complex analysis, measure theory, ergodic theory, numerical analysis and its computational implementation, topology, number theory, etc. Roughly speaking, the theory of dynamical systems consists in the rigorous study of one, several, or even infinitely many features associated to a process that depends intrinsically on parameters and that evolves when an independent variable (that we call time for obvious reasons) varies. Most of the problems in this context arise from physics (movement of celestial bodies, heat evolution in a rigid body...), biology (evolution in a structured population, neuroscience, cell growth...), economy (generational phenomena, market prices evolution...), chemistry (chemical reactions), new technologies (complex networks) or from mathematics themselves (graph theory, fractals, chaos...).
The main objects of interest in any dynamical system depending on parameters, no matter in which specific framework occurs, are the following:
• The phase portrait for a fixed parameter of the system, which serves to determine the future value of the system features (or system states) in the phase space based on their present values;
• The bifurcation diagram in the parameter space, which is meant to describe how a specific feature of the system varies as we move the parameters. In this respect it deserves particular attention the bifurcation phenomena that occur at those parameters which lie on the boundary between qualitatively different phase portraits.
Understanding these objects is formalized into different statements or challenges depending on the context. In particular there is a preliminary division based on whether the evolution of the process is continuous (real time) or discrete (natural or integer time), but there are other relevant considerations as the dimension of the problem (i.e., number of features we wish to observe), the topology of the phase space, the type of bifurcations in the parameter space, etc. The origin of the discrete version goes back to the studies of the chaotic dynamics by A.N. Sharkovskii (1964) and T.Y. Li and J.A. Yorke (1975) for the real case, together with the works of Cayley about Newton's method (1879), the memoirs of P. Fatou and G. Julia (1920), and the notes of Orsay written by A. Douady and J.H. Hubbard (1982). Both scenarios real and complex show that very simple models in low dimension can exhibit extremely rich dynamics. In this context the present proposal focuses in problems related to topological and combinatorial dynamics and the description of the period set of continuous maps in graphs and trees. We also want to study the topological and analytical properties of the connected components of the Fatou set and the dynamics on their boundaries, the existence and distribution of wandering domains inside the Fatou set and the description of the parameter space and its bifurcations.
Main activities
Weekly joint seminar: For the duration of the program, different dynamical systems seminars in the Barcelona area will merge into this seminar at the CRM.
Scientific committee
Núria Fagella 
Universitat de Barcelona 
Francesc Mañosas 
Universitat Autònoma de Barcelona 
Michal Misiurewiz 
Indiana University – Purdue University Indianapolis 
Robert Roussarie 
Université de Bourgogne 
Gwyneth Stallard 
Open University 
Organizers
Peter De Maesschalck 
University of Hasselt 
Antonio Garijo 
Universitat Rovira i Virgili 
Xavier Jarque 
Universitat de Barcelona 
David Juher 
Universitat de Girona 
Boguslawa Karpinska 
Technical University of Warsaw 
Lubomir Snoha 
University of Bratislava 
Joan Torregrosa 
Universitat Autònoma de Barcelona 
Jordi Villadelprat 
Universitat Rovira i Virgili 
Invited visiting researchers
Jozef   Bobok   Czech Technical University in Prague   01/03/2020   28/03/2020  Henk   Bruin   University of Vienna   03/02/2020   14/02/2020  Claudio   Buzzi   Universidade Estadual Paulista   02/02/2020   04/03/2020  Peter   De Maesschalck   Universiteit Hasselt   03/02/2020   22/02/2020  Kealey   Dias   City University of New York   02/02/2020   22/02/2020  Igsyl   Domínguez   Pontificia Universidad Católica de Chile   02/02/2020   27/04/2020  Vasiliki   Evdoridou   The Open University   15/04/2020   30/04/2020  Nuria   Fagella   Universitat de Barcelona   02/02/2020   20/04/2020  Xavier   Jarque   Universitat de Barcelona   02/02/2020   20/04/2020  Dominik   Kwietniak   Jagiellonian University in Kraków   15/03/2020   28/03/2020  Kirill   Lazebnik   Caltech University   15/04/2020   26/04/2020  Jérôme   Los
  Université d'AixMarseille   17/02/2020   31/03/2020  Michal   Misiurewicz   Indiana University   02/02/2020   28/03/2020  Piotr   Oprocha   AGH University of Science and Technology   15/03/2020   29/03/2020  Daniel   Panazzolo   Université de HauteAlsace   16/02/2020   01/03/2020  Salomón   Rebollo Perdomo   Universidad del BíoBío   29/01/2020   29/02/2020  Miriam   Romero   Universidad Autónoma del Estado de Morelos   03/02/2020   30/04/2020  Robert   Roussarie   Université de Bourgogne   09/02/2020   22/02/2020  Mitsuhiro   Shishikura   Kyoto University   01/02/2020   08/02/2020  Lubomír   Snoha   Matej Bel University   01/03/2020   29/03/2020  Bishnu Hari   Subedi   Tribhuvan University   02/02/2020   27/04/2020  Jordi   Villadelprat   Universitat Rovira i Virgili   03/02/2020   26/04/2020 


For inquiries about the programme please contact the research programme's coordinator Ms. Núria Hernandez at nhernandez@crm.cat
EMS GRANT:
The EMS offers some travel grants to young mathematicians from lessfavoured regions within the geographical area of EMS membership for presenting results at conferences or attending courses, or for research stays in foreign countries, normally up to a maximum of 900 euros in each case or 500 euros for trips within Europe.
Eligible researchers should use this online form in order to apply for travel grants.
The applications must be submitted by September 30^{th}, 2020.
Acknowledgements
